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A related uniqueness theorem of Helmut Wielandt states that the complex gamma function and its scalar multiples are the only holomorphic functions on the positive complex half-plane that obey the functional equation and remain bounded for complex numbers with real part between 1 and 2. [68] Other complex functions that interpolate the factorial ...
The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n.For example, 5! = 5×4×3×2×1 = 120. By convention, the value of 0! is defined as 1.
The factorial number system is sometimes defined with the 0! place omitted because it is always zero (sequence A007623 in the OEIS). In this article, a factorial number representation will be flagged by a subscript "!". In addition, some examples will have digits delimited by a colon. For example, 3:4:1:0:1:0! stands for
Fuss–Catalan number; Central binomial coefficient; Combination; Combinatorial number system; De Polignac's formula; Difference operator; Difference polynomials; Digamma function; Egorychev method; Erdős–Ko–Rado theorem; Euler–Mascheroni constant; Faà di Bruno's formula; Factorial; Factorial moment; Factorial number system; Factorial ...
Thomae's function: is a function that is continuous at all irrational numbers and discontinuous at all rational numbers. It is also a modification of Dirichlet function and sometimes called Riemann function. Kronecker delta function: is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise.
In number theory, a Wilson prime is a prime number such that divides ()! +, where "!" denotes the factorial function; compare this with Wilson's theorem, which states that every prime divides ()! +. Both are named for 18th-century English mathematician John Wilson ; in 1770, Edward Waring credited the theorem to Wilson, [ 1 ] although it had ...
These symbols are collectively called factorial powers. [2] The Pochhammer symbol, introduced by Leo August Pochhammer, is the notation (), where n is a non-negative integer. It may represent either the rising or the falling factorial, with different articles and authors using different conventions.
This is in contrast to binary operations, which use two operands. [2] An example is any function : , where A is a set. The function is a unary operation on A. Common notations are prefix notation (e.g. ¬, −), postfix notation (e.g. factorial n!